Florence Nightingale: The compassionate statistician

Florence Nightingale died a hundred years ago, in August 1910. She survives in our imaginations as an inspired nurse, who cared passionately for injured and dying soldiers during the Crimean war, and then radically reformed professional nursing as a result of the horrors she witnessed. But the "lady with the lamp" was also a pioneering and passionate statistician. She understood the influential role of statistics and used them to support her convictions. So to commemorate her on the centenary of her death, we'll have a look at her life and work as a statistician.

A privileged intellect

A young Florence Nightingale

Florence Nightingale was born in 1820 into a liberal-humanitarian household. Her solidly upper-middle-class family were intellectually adventurous free thinkers who endorsed women's education. Various tutors taught Florence and her elder sister Parthenope arithmetic, botany, French and geography, as well as drawing and piano. Their father, William Edward Nightingale, a graduate of Trinity College, Cambridge, gave them a university education at home, teaching them mathematics, Latin and Greek. After Florence had finally begun this rigorous education at the age of 12, she wrote that "I have the most enormous desire of acquiring. For seven years of my life I thought of little but cultivating my intellect." Nightingale's upbringing thus nourished and stimulated her enthusiasm of mathematics. By the time she was nine years old, she was already organising data from garden fruits and vegetables in numerical tables.

Florence's early life was privileged not just in an intellectual sense. After her father inherited an enormous fortune from his uncle, he settled down to the life of a country gentleman. The family had a 14-bedroom house in Lee Hurst in Derbyshire (now the Derbyshire Royal Infirmary) where they stayed in the summer and a Georgian mansion in Embley Park in Hampshire (now the Hampshire Collegiate School) that came with 100 acres, where they lived most of the year. They also had rooms in Mayfair for the spring and autumn London seasons. The family toured the continent attending operas in Italy and socialising in Paris.

In these exalted circles Nightingale met a number of Victorian literati, including the mathematician Charles Babbage. She was fascinated with numbers at an early age and at twenty wanted further tuition in mathematics. She began receiving two-hour instructions from a Cambridge-trained mathematician. Her mathematical aptitude fuelled her predilection for statistics. In the mornings Nightingale would study material on the statistics of public health and hospitals, and eventually she accumulated a formidable array of statistical information. Her enjoyment was so immense, she found the sight of a long column of figures "perfectly reviving".

Victorian statistics

Nightingale was not alone in her passion for numbers, for the Victorians were avid statisticians. The word "statistics" had been introduced to the English language in 1798 by the Scottish landowner Sir John Sinclair in his Statistical Account of Scotland. Initially, politicians were interested in matters of the state, such as land ownership and the population, mainly to determine the numbers who were liable for the military and to fix the rates of taxation. But by the late 1820s and early 1830s, MPs embraced the newer fields of vital and social statistics. With the aid of the newly developed steam printing press and railway, colossal amounts of data could be collated and disseminated by state agencies, organisations and individuals, and used to study mass phenomena including poverty, disease and suicide. This, in turn, led to a wide-spread dissemination of statistical information by the middle-classes who provided lectures, health tracts and medical advice in the popular press, self-help books and novels. Journalists, social reformers and MPs used statistics to floor their opponents.

Florence Nightingale in the 1850s

Many of the early Victorian statisticians regarded statistics as more than the mere collection of social data or a set of techniques. For them statistics was "the new study of man in society", which would enable them to make predictions about the social conditions of the poor and the labouring classes. The health reformers and vital statisticians, William Farr and Edwin Chadwick, undertook statistical analyses, which led to the creation of the Public Health Acts to improve the deleterious circumstances of the poor, especially in the industrialised cities where perilous living conditions threatened the lives of so many Victorians.

Statistics as the word of God

Perhaps surprisingly to a modern mind, Florence's own statistical ideas were an integral part of her religious beliefs. As a child she had a desire to nurse the sick and remembered that her daydreams were all about hospitals; she thought these daydreams symbolised that "God had called her to Him in that way". This calling meant, much to her relief, that she would not have to be tied to a life of society and the stifling constraints of a Victorian upper-middle class marriage. The divine inspiration gave her the opportunity to develop her intellectual pursuits. By the time she was in her twenties, she had rejected the supernatural and miraculous underpinnings of Christianity, and awaited the coming of a female Christ.

Nightingale proposed a form of religion in which human beings actively contributed to the realisation of God's law through their work. Statistical laws, since they reveal patterns in the world around us, had the power to reveal God's providential plan: "to understand God's thoughts, we must study statistics for these are the measure of His purpose". This ideology, which was rooted in the ideas of the eighteenth-century clergyman and natural philosopher William Derham, turned the statistical study of natural phenomena into a moral imperative and religious duty: it was the surest way of learning the divine plan and then acting in accordance with it. Moreover, her religious outlook turned the study of statistics from a slightly questionable activity for a lady into a legitimate pursuit within a religious Victorian culture.

The Crimean war

In October 1853 the conflict between Russia and an alliance of European countries over the declining Ottoman empire turned into a fully-fledged war, fought in the Turkish region of Crimea. Nightingale volunteered her services and was eventually asked by her lifelong friend and Secretary at War, Sidney Herbert, to be "Superintendent of the female nursing establishment in the English General Military Hospitals in Turkey" for the British troops fighting in the Crimean war. She took a group of thirty-eight nurses with her.

Nightingale at the Scutari hospital, from an 1856 lithograph.

Once Nightingale arrived in the Crimea, she found herself amid utter chaos in the hospital at Scutari: there were no blankets, beds, furniture, food, or cooking utensils, and there were rats and fleas everywhere. Nightingale was dismayed not only by the appalling lack of sanitation, but also the statistical carelessness she found in the military hospitals. The medical records were in a deplorable state, as none had been maintained in a uniform manner. Moreover, there was a complete lack of co-ordination among hospitals and no standardised or consistent reporting. Each hospital had its own system of naming and classifying diseases, which were then tabulated on different forms, making comparisons impossible. Even the number of deaths was not accurate; hundreds of men had been buried, but their deaths were not recorded.

One of the first books Nightingale wrote, Notes on Matters Affecting Health, Efficiency, and Hospital Administration of the British Army (1858), provided statistical evidence that showed just how much of the mortality was due to the conditions of the hospitals. Whilst her use of the word "notes" might suggest that it is a small collection of her thoughts, the book is, in fact, 850 pages long. She worked incessantly on this book and "sometimes for twenty-four hours out of 24", finishing it in a record-breaking two years. In it she compared the death rates of the army in peacetime with the civilian rate and concluded that, "our soldiers are enlisted to die in barracks".

The statistical data Nightingale collected during the first seven months of the Crimean campaign were later analysed with the help of William Farr, Britain's foremost statistician at the time. Farr had been recruited to compile the statistical records of the General Register Office, which records vital information such as births, deaths and marriages, shortly after it was first set up in 1832. His legacy with his colleague, the epidemiologist Thomas Rowe Edmonds, was "the creation of the modern discipline of vital statistics and using these statistics to assess public health and welfare".

A statistical partnership

It was Nightingale's close collaboration with Farr that led to some of her most important statistical work. When they met at a dinner party at the home of Colonel Alexander Tulloch in the autumn of 1856, she had just returned from the Crimea a national heroine and recognised that if such suffering were never to happen again, the Army Medical Service, and if necessary the army itself, must be reformed. She was about to begin her campaign for reform in the Army Medical Department when they met. Farr was sympathetic to her ideas. They began a correspondence that would continue for twenty years, writing some four hundred letters between them.

William Farr in 1870.

Queen Victoria summoned Florence Nightingale to Balmoral the week after she returned from the Crimea. She was keen to meet The Queen and Prince Albert, an emphatic supporter and patron of science and statistics, and she successfully procured their support for a Royal Commission on the health of the army. On her recommendation Farr was appointed a member, as was the army doctor and statistician, Thomas Graham Balfour, FRS.

Nightingale relied on Farr for the analysis of the army reform returns of death and disease (though she did eventually become competent at undertaking statistical analyses on her own), and for some of his tactics of using mortality statistics as argumentative tools. Farr benefited from Nightingale's knowledge of nursing practices in major hospitals and her politically influential connections — her maternal grandfather sat in the House of Commons for nearly 50 years as an abolitionist, and her family's neighbour at Embley Park, Lord Palmerston, became Prime Minister during the Crimean War. Their twinned desires to see reforms in the Army Medical Department led to a fulfilling and productive professional relationship. They collaborated in the preparation of hospital statistics for her books Notes on Hospitals (1859) and Introductory Notes on Lying-in Institutions (1871).

Dying in the barracks

The statistical evidence from Nightingale's mortality rates in civilian and military hospitals showed that unsanitary living conditions leading to endemic diseases such as typhus, typhoid and cholera were indeed the principal reason for such high mortality rates. Moreover, the Crimean data revealed that during the war more troops died from these diseases and unsanitary living conditions than in London during the plague of 1655. Nightingale and Farr discovered there was an annual mortality rate of 60% for these soldiers. Between the ages of 25 and 35, the mortality rate in military hospitals was double that in civilian life.
Later on, Nightingale and Farr demonstrated that three times as many soldiers died at home and abroad during peacetime than when they were at war because of overcrowding and filth in the industrialised cities.

Nightingale wrote a report based on the army medical statistics and sent it as a confidential communication to the War Office and Army Medical Department. Eventually, the army adopted Farr's classification of disease, with modification. One of the main outcomes of the statistical aspect of the Royal Commission was the creation of a department of Army Medical Statistics. The Surgeon-General and President of the Statistical Society of London (from 1888 to 1890), Thomas Graham Balfour, undertook statistical analyses of material relating to the Army Sanitary Commission of 1857 and its report of 1858. A year later he was appointed to work in the new Army Medical Statistics Department that Nightingale and Farr established. In this capacity, he compiled the first four volumes of Statistics of the British Army.

The polar area graph

Farr was one of the first statisticians to make extensive use of circular diagrams and other pictorial aids. Like Nightingale, Farr understood that the use of visual aids and graphs should be aimed at those who were not accustomed to looking at statistical data or life tables. Nightingale developed a flair for devising graphic methods, including her well-known polar area graph, which was similar to the pie chart created by the Scottish economist William Playfair in 1801. This polar area graph is equivalent to a modern circular histogram, used for illustrating grouped cyclic data. It was cut into twelve equal angles, where each slice represented one month of the year, which, as you can see, revealed changes over time. (The graph is often mistakenly referred to as the coxcomb, although Nightingale herself used the term for specially printed copies of her booklet, Mortality of the British Army, which contained the graph.)

Nightingale's most famous polar area diagrams: Diagram of the causes of mortality in the army in the east.

If we look at the polar area graph, we can see that the area of each coloured wedge, measured from the centre, is in proportion to the statistic it represents. The blue outer wedges represent the deaths from contagious diseases, such as cholera and typhus. The central red wedges show the deaths from wounds. The black wedges in between represent deaths from all other causes. If this rate had continued, and troops had not been replaced frequently, then disease alone would have killed the entire British Army in the Crimea. Nightingale's graph not only dramatised the extent of the needless deaths among the soldiers during the Crimean War, but it was used as a tool to persuade the government and medical profession that deaths were preventable if sanitation reforms were implemented in military and civilian hospitals.

Hospitals at home

Nightingale's reformatory spirit did not restrict itself to military hospitals. Her investigation of London's hospital statistics in 1858 confirmed that the record-keeping needed to be revised. She found that in addition to just simple carelessness in the collation of statistical information, there was a complete lack of scientific coordination. For example, hospital statistics gave very little useful information on the average duration of hospital treatment or on the proportion of patients who recovered compared with those who died.

As Statistical Superintendent to the General Registrar Office, Farr had found it deeply troubling that there were so many inconsistencies in the reporting of deaths in English hospitals, which did not use a standard system to classify disease. A Statistical Society Committee was set up for the campaign to keep hospital statistics in a uniform scheme that would permit comparative studies. Nightingale proposed that the same medical forms be used in all hospitals. After the International Statistical Congress, held in London in 1860, endorsed Nightingale's plans she convinced London and a few Parisian hospitals to comply with her forms. In 1861 the results of these hospital reports were published in the Journal of the Statistical Society of London in 1862.

Nightingale's skills in reporting and illustrating statistical data for sanitary reform in military and civilian hospitals led William Farr to nominate her as the first woman to be elected a Fellow of the Statistical Society of London in October 1858. In the same year she was also elected to the Statistical Congress, and she was made an honorary foreign member of the American Statistical Association in 1874.

Nightingale's legacy

By the end of the Victorian era politicians could no longer afford to ignore the overwhelming importance of the role of statistics in government, especially as much of which was inconsistent and needed to be standardised. However, this did not happen on a large scale until 1918, in the aftermath of the Great War, owing to the work Karl Pearson, his colleagues and students undertook during the war. Another of Nightingale's ideas, to set up a department of statistics at the University of Oxford, found partial fruition just after her death, when a Department of Applied Statistics was set up at University College London in 1911. More than a century would pass before Oxford University renamed their Department of Biomathematics the Department of Applied Statistics in 1988.

Although Florence Nightingale is rightly acknowledged and highly venerated for her role in reforming nursing in the mid-nineteenth century, she clearly deserves more recognition than she has received for revolutionising nursing through her use of statistics. Her investigative statistical work led to a decline in the many preventable deaths that occurred throughout the nineteenth century in English military and civilian hospitals. Her pioneering use of evidence-based medicine became a powerful directive in garnering support from the medical community and the government.

Nightingale's statistical innovations and achievements are as important in the twenty-first century as they were in the mid-nineteenth century. Certainly, making statistical data accessible by using diagrams and charts is imperative for the medical sciences. Moreover, the development of randomised clinical trials in the mid-twentieth century and the growing reliance on evidence-based medicine in the twenty-first century demand an understanding of contemporary statistical methods, which will enable nurses to make informed decisions about current medical research and their patients.

About this article

This is a modified version of an article which first appeared in Radical Statistics, 102 (2010) pp 17-32.

Eileen Magnello trained and worked as a statistician before doing her PhD in the history of science at St Antony's College, Oxford University. She has published extensively on the statistical innovations and the life of the late-Victorian mathematician Karl Pearson. Her long-standing interest on the role of Victorian vital statistics in the promulgation of public health in the nineteen century has led to her interest in Florence Nightingale's use of statistics in her development of the nursing profession. Magnello is a Research Fellow in the Department of Science and Technology Studies at University College London. Her most recent book is Introducing statistics: A graphic guide, reviewed on Plus, and she is currently writing a book on the statistical life and work of Florence Nightingale.

Comments

I doubt the diagram would be as famous and respected as it is if it had been as flawed as the OP suggests!

A radial representation is a different type of graph entirely.

The text is correct: in these diagrams the area is proportional to the statistic, as in all "polar area" and pie charts.

If there is a weakness, it is that all areas are (as the text says) "measured from the centre" - so the area which represents deaths from wounds is the blue+pink+black, not just the blue bit (as you'd intuitively expect - so there is no "order" to the segments).

It's obvious if you look at the original figures:
For example, in January 1855 deaths from diseases were 2761, from wounds were 83, from all other causes 324.
If the chart was radial, pink+black would only come 1/7 (407/2761) of the way to the edge.

Whereas actually, pink+black should come about 1/3 of the way out (root2761/pi)/(root407/pi). [if my rusty maths is right]

Florence Nightingale's text is in error about the area representation ("If we look at the polar area graph, we can see that the area of each coloured wedge, measured from the centre, is in proportion to the statistic it represents.")

The radius of the wedge is in proportion to the statistic it represents.

It's a good point and it shows how statistical representations may actually deceive by placing a particular emphasis. If the statistics are proportional to the radii then those shown on the outside of the circle will have a bigger area and therefore seem more important. Would Nightingale's plots have been quite so persuasive if she had put deaths through combat on the outside and therefore had much bigger red patches in her graphs?